Abstract
The author examines the first-order in overlap approximation to the Adams-Gilbert equation derived previously by Kunz (1969). It is shown that this approximation is far more general than previously assumed and is an exact member of the family of local orbitals equation derived by Gilbert (1964). The relationship of this result to the method proposed by Anderson (1968) is discussed, and a class of situation is found where the present formalism may be preferable. Approximations to the present case are discussed and illustrated with a simple calculation for the He2 molecule.